Michael is 2 times as old as Tiffany. 36 years ago, Michael was 8 times as old as Tiffany. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Tiffany. Let Michael's current age be $m$ and Tiffany's current age be $t$ The information in the first sentence can be expressed in the following equation: $m = 2t$ 36 years ago, Michael was $m - 36$ years old, and Tiffany was $t - 36$ years old. The information in the second sentence can be expressed in the following equation: $m - 36 = 8(t - 36)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $t$ and substitute it into our second equation. Solving our first equation for $t$ , we get: $t = m / 2$ . Substituting this into our second equation, we get: $m - 36 = 8($ $(m / 2)$ $- 36)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 36 = 4 m - 288$ Solving for $m$ , we get: $3 m = 252$ $m = \dfrac{1}{3} \cdot 252 = 84$.